Timeline for Examples of patterns that eventually fail
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 16, 2016 at 11:54 | comment | added | jochen | It may spoil some joke (which, if there is one, I don't get), but would it make sense to to change the definition of $f$ in the question to $f(n) = n^2 - n + 41$? I believe the form with the "$-n$" is more traditional and it moves the first counter example from $n=40$ to $n=41$. | |
| Aug 17, 2016 at 17:01 | comment | added | Red Banana | @Tib One day I went to buy two items. First item's cost was 2.00, the other item's cost was 3.45. The person in there needed a calculator to know the sum. | |
| Sep 23, 2014 at 1:38 | comment | added | ncmathsadist | I had my introCS students going on this today.... I subbed in for a few integer and heard, "We can prove this by induction!" Snicker. | |
| Jul 2, 2013 at 23:10 | comment | added | ncmathsadist | Snicker, @JMCF125, very good! | |
| Jul 2, 2013 at 16:24 | comment | added | JMCF125 | +1 BTW, isn't this that expression that fooled Euler? | |
| Feb 16, 2013 at 4:41 | history | edited | Austin Mohr | CC BY-SA 3.0 | added 49 characters in body |
| Jun 3, 2012 at 0:22 | comment | added | ncmathsadist | Naturally, but many ppl don't pay attention, which is my point. | |
| Jun 2, 2012 at 23:24 | comment | added | MJD | $40^2+40+41$ is also clearly divisible by 41. | |
| Feb 25, 2012 at 1:03 | comment | added | ncmathsadist | This is correct but you'd be surprised at how few people think of that broadly obvious solution. | |
| Feb 24, 2012 at 18:10 | comment | added | Tib | @MikeBoers: That's what I was trying to say. | |
| Feb 23, 2012 at 20:45 | comment | added | Mike Boers | @Tib: It is easy to check if you push them in the right direction. $41^2 + 41 + 41$ is clearly divisible by 41. | |
| Feb 22, 2012 at 3:33 | history | made wiki | Post Made Community Wiki by Zev Chonoles | ||
| Feb 21, 2012 at 17:27 | comment | added | Tib | This doesn't really satisfy condition (2.) of the original question. No sane person needs a computer to check the $n=41$ counterexample. | |
| Feb 21, 2012 at 3:30 | comment | added | The Chaz 2.0 | It appears to be a prime number generating polynomial. Appears... (edit) It also appears that @Seth and I saw this at the same time! | |
| Feb 21, 2012 at 3:29 | comment | added | Seth | @Dason: If $f(n) = n^2 + n + 41$, is $f(n)$ prime for n = 1, 2, 3,...? | |
| Feb 21, 2012 at 3:07 | comment | added | Dason | The chestnut being what exactly? | |
| Feb 21, 2012 at 0:28 | history | answered | ncmathsadist | CC BY-SA 3.0 |